One known method to extend the range of optical metrology applications for interferometry is to measure the interferometric phase at two distinct wavelengths.
When monochromatic light is made to interfere with itself in a two-beam interferometer, the output intensity as measured by a square-law detector is proportional to a function h: EQU h(mx)=cos.sup.2 (.pi.m), (1)
where m is the fringe order, equal to one over 2.pi. times the relative phase of one beam to the other. The optical path difference between the two beams is related to the fringe order by EQU L=m.lambda./2, (2)
where L is the one-way optical path difference, including the refractive index, and .lambda. is the vacuum wavelength. In that h is a periodic function, the integer part of m cannot be determined by inverting Eq. (1). Interferometry typically provides only the fractional part f(m) of the fringe order, with the consequence that only changes of the length L, and not its absolute value, can be measured directly. This integer fringe-order ambiguity limits the usefulness of interferometry in many applications.
The purpose of multiple-color, or multiple-wavelength, interferometry is to measure the integer part of m so that the entire length L may be directly measured with great precision in terms of the vacuum wavelength.
Analytical procedures for determining lengths from multiple-wavelength interferometry exist in a variety of forms. One such procedure employs the concept of synthetic wavelengths, derived from differences in pairs of wavelengths in the interferometer, and the corresponding synthetic fringe orders, derived from differences in the phase measurements for these wavelengths.
By example, and considering three optical wavelengths .lambda..sub.1, .lambda..sub.2, and .lambda..sub.3, there are three possible synthetic wavelengths defined by EQU 1/.LAMBDA..sub.ij =1/.lambda..sub.i -1/.lambda..sub.j, .lambda..sub.j &gt;.lambda..sub.i. (3)
It is noted that a synthetic wavelength can be made much larger than a visible wavelength by choosing appropriate pairs of wavelengths .lambda..sub.i, .lambda..sub.j. The fractional part of the corresponding synthetic fringe orders M.sub.ij are obtained from the differences in optical fringe orders m.sub.i and m.sub.j as: EQU M.sub.ij =m.sub.i -m.sub.j ( 4)
The length L may be calculated from a synthetic wavelength measurement as: EQU L=(M.sub.ij .LAMBDA..sub.ij)/2. (5)
The larger the synthetic wavelength the greater the range of distances L that can be accommodated without possibility of error due to an integer ambiguity in the value of M.sub.ij. Conversely, the precision in the measurement of L is optimized when using relatively small synthetic wavelengths.
The following prior art discuss various aspects of conventional two-wavelength interferometry.
As described in U.S. Pat. No. 4,832,489, issued May 23, 1989, to J.C. Wyant et al., a two-wavelength phase-shifting interferometer employs two laser sources for reconstructing steep surface profiles, such as aspheric surfaces. A 256 .times.256 detector array is used and the computes an equivalent phase independently each detector.
The following articles discuss various aspects of employing a synthetic wavelength for surface profilometry.
In an article entitled "Contouring Aspheric Surfaces Using Two-Wavelength Phase-Shifting Interferometry" by K. Creath, Y. Cheng, and J. Wyant, Optica Acta, 1985, Vol. 32, No. 12, 1455-1464 there is described two-wavelength holography using an argon-ion laser and a He-Ne laser. Two wavelengths from the argon-ion laser (0.4880 micrometers or 0.5145 micrometers) were employed in conjunction with a single wavelength (0.6328 micrometers) from the He-Ne laser to yield equivalent wavelengths of 2.13 micrometers and 2.75 micrometer. An uncoated test surface was placed in one arm of the interferometer and interferograms were recorded using a 100.times.100 diode array.
In an article entitled "Absolute Optical Ranging with 200-nm Resolution" by C. Williams and H. Wickramasinghe, Optics Letters, Vol. 14, No. 11, Jun. 1, 1989 there is described optical ranging by wavelength-multiplexed interferometry and surface profiling said to be carried out on an integrated circuit structure. A pair of GaAlAs single-mode diode lasers are used as optical sources.
In an article entitled "Two-wavelength scanning spot interferometer using single-frequency diode lasers" by A. J. de Boef, Appl. Opt., Vol. 27, No. 2, Jan. 15, 1988 (306-311) there is described the use of two single frequency laser diodes to measure the profile of a rough surface. The two wavelengths are not time-multiplexed but are instead continuously present.
In an article entitled "Two-Wavelength Speckle Interferometry on Rough Surfaces Using a Mode Hopping Diode Laser" by A. Fercher, U. Vry and W. Werner, Optics and Lasers in Engineering 11, (1989) pages 271-279 there is described a time-multiplexed two-wavelength source consisting of a single mode diode that is switched between two adjacent oscillation modes. The switching is accomplished by pump-current modulation with the diode thermally tuned to a region near a so-called "mode hop", that is, near a region where the diode output readily switches from one wavelength output to another. This technique is said to have enabled the profiling of a ground lens surface.
As was previously stated, the larger the synthetic wavelength, the greater the range of distances (L) that can be accommodated without possibility of error due to an integer ambiguity in the value of the synthetic wavelength fringe order (M.sub.ij).
However, the precision in the measurement of L is best when small synthetic wavelengths are used.
It is thus an object of the invention to provide optical metrology apparatus, including apparatus for determining a distance between two surfaces, that employs a plurality of synthetic wavelengths of different size.
It is a further object of the invention to provide optical metrology apparatus, including apparatus for determining a distance between two surfaces, that employs a plurality of synthetic wavelengths of different size, the synthetic wavelengths being derived from three optical wavelengths emitted from at least one and preferably two multi-mode laser diodes.
It is another object of the invention to provide optical metrology apparatus, including apparatus for determining a distance between two surfaces, that employs a plurality of synthetic wavelengths of different size, using progressively smaller synthetic wavelengths to improve the precision of measurement while retaining the dynamic range made possible by a large synthetic wavelength.